HYDRAULICS BRANCH OFFICIAL FILE COPY

1 ` SYMPOSIUM 1970

STOCKHOLki i

' I ~ i

FREQUE14CY AND AMPLITUDE OF PRESSURE SURGES GENERATED

. BY SWIRLING FLOW

I H. T. Falvev U. S. Bureau of Denver, Colorado

I Heal, Hydraulic Research Section Reclamation USA

J. J. Cassidy University of Columbia, Missouri Professor of Civil Engineering Missouri USA

SYNOPSIS This paper reports on the investigation of swirling flow through tubes. Fre-

quencies and amplitudes of pressure surges produced by the swirling flow were

measured and found to be essentially independent of viscous effects for Reynolds

numbers larger. than 1x105. Dim;nsionless frequency and pressure par_.rrr2t2rs as

well as the onset of surging were correlated with the parameter SO!pQ2 Where sl and

Q are respectively the fluxes of angular momentum and volume through the tube, D

is the tube diameter and p is the fluid density. Relative length and shape of the

j tube were also found to be important.

The results of the study were used to analyze a particular draft tube for

potential surging. Using performance data obtained from the model of the turbine

and draft tube, a icyloil of sur-ye-free operation was outlined on the efficiency

I hill for the unit. Comparison was made between measured poorer swings and the

predicted pressure fluctuations in the draft tube.

RESUME Cette communication a trait a une recherche sur un courant tourbillonnaire

jpassant dans des tubes. Les frequences et les amplitudes des surpressions creees

j par le courant tourbillonnaire ont kt mesurees et trouvees essentiellement i -

indepandantes des effets de viscosite pour des nombres de Reynolds superieurs e

j 1x105. Des parametres sans dimension lies a la frequence et a la pression et

1'etablissement de la surpressions ont Le relie's au parametee QD/pQ2 ou ,i et Q

sont respectivement les flux du moment angulaire et du volume dans le tube, D le

diame-tre du tube et p la densite du fluide. On a trouve que la longueur relative

et la forme du tube sont egalement importantes.

On a utilise les resultats de cette etude pour analyser l'etablissement de la

surpressions dans une conduite d ecoulement particuliere. En utilisant les donnees

de fonctionnement obtenues a partier d'un modem de turbine et de conduite

d-ecoulement, on a ,rouve un domaine de marche mans surpressions sur le diagramme

de rendement de 1'unite. On a compare les resultats des mesures des amplitudes de

puissance et ceux des calculs des fluctuations de pression dans la conduite

i d'ecoulement.

INTRODUCTION

Draft-tube surging has been recognized as a problem in the operation of

hydro-power plants for several decades [1]. History shows that the attack on

draft-tube surging has been one of alleviation rather than prevention. New units

are placed in operation and if objectionable surging occurs within the operating

range various types of remedial action are attempted or, if possible, operation

is not permitted in the critical range. However, because of automation of the

generating systems, plants are frequently required to operate over a wide range

of turbine gate openings. Remedial measures including air admission to the draft

tube or the placement of fins in the draft-tube throat are only occasionally

successful. If it were possible to predict the possibility of surging prior to

installation and operation of a unit, considerable advantage could be realized.

It appears to be generally accepted that draft-tube surging arises as a

result of rotation remaining in the water as it leaves the turbine runner and

enters the draft tube [2]. Moreover, the phenomenon is complicated by many fac-

tors including vaporization of the water, geometry of the turbine and draft tube,

and the dynamic characteristics of the penstock and electrical network. Swirling

flow has been investigated analytically and experimentally by several people in

the field of fluid mechanics [3,4,5,6]. These studies have shown that when a

fluid flows in a swirling fashion (axial flow with superimposed rotation) the

J

resulting flow pattern depends upon the relative amount of rotation in the

J fluid.

If the flux of angular momentum entering the tube is sufficiently large as com-

pared to the flux of linear momentum, a reversal in flow direction occurs along

the centerline of the tube [3]. For large Reynolds numbers the flow becomes

unsteady forming a helical vortex with the reversed flow occurring along the

spiral core of the vortex [7]. This phenomenon is known as "vortex breakdown" in

the fluid mechanics literature and as draft-tube surging in the hydraulic-machin-

ery literature [8].

This paper describes a study initiated in order to investigate the character-

istics of swirling flow in tubes and to correlate these characteristics with the

occurrence and nature of draft-tube surging.

THE Rncrr cTiinv

Because of the excessive number of variables which could be involved it

was not only desirable but necessary to simplify the experimental model as much

as possible. Air was used as the working fluid in order to eliminate the possible

effects of a two-phase flow. No turbine runner was installed in order to simplify

geometry. Instead the air entered the tube (Figure 1) radially through wicket-

gate type vanes. It was possible to accurately determine the amount of swirl

imparted to the flow as it entered the tube. The angle between the vanes and a

radial line could be set at any angle between 0° and 82°. At 00 the vanes were

2 g 1

its ig i

aft

)e, iny-

i

id.

in in-

ter-

ie

L

Flow -tea Wicket Gate or Inlet Vane

Smoke Injecter Here _

Flow _

D

-enter Line

Stilling Chamber

FIGURE 1 EXPERIMENTAL APPARATUS SHOWING STRAIGHT TUBE

or

a

FIGURE 2 DEFINITION SKETCH OF INLET FLOW TO TUBE OR RUNNER ible

Iify

1 3

Ue

radial and no rotation was applied to the flow (Figure 2). Overall configuration

of the apparatus is shown in Figure 1 and is described in more detail by Cassidy

[7]. Clear plastic was used in construction to facilitate flow visualization

with smoke. Pressures at points on the tube wall were measured using pressure

cells and a root-mean-square meter. Frequencies of the unsteady pressure were

determined using an oscilloscope with a retentive screen.

Flow through three types of tubes was studied:

1) circular tubes of uniform diameter; 2) a model of a draft tube used in

Fontenelle Dam; 3) an expanding cone having the same length-to-area relation-

ship as the draft tube.

ANALYSIS

It was assumed that, for a particular draft-tube shape, the root-mean-square

amplitude AP and frequency f of the unsteady pressure surge are both functions of

the fluid density p and viscosity v, draft-tube diameter D and length L, discharge

Q, and flux of angular momentum Q. Standard techniques of dimensional analysis

yield the following functional relationships

D4AP = ~ /1Z D L IR ) (1) ~2 s n2 — D

7c,93 3 = ~2(p D ) ~ ) (2)

wherelR is the Reynolds number 4Q/nDv.

The angular momentum flux Q enterinq the tube was computed as (see Figure 2)

11 to OR V. sin a (3)

in which Q = SBNVo.. The variables S, a, Vo, and R are defined in Figure (2);

N is the number of vanes around the inlet; and B is the dimension of the vanes

perpendicular to the plane of Figure 2. The momentum parameter contained in

Equations (1) and (2) is then computed as

rLD _ DR sin a (4) pQ _ BNS

and is seen to be a function of geometry only for the particular inlet conditions

of this study. In all experiments the momentum parameter nD/pQZwas calculated

according to Equation (4).,

~s 4 S 1

PA

V%

a.) Steady Swirling Flow, no b.) Stagnation Point at the c.) Fully Developed Surging, surging, D=3.46 inches, Centerline With Surging SID /pQ2=0.454, D=6.13 inches, L/D=7.15, QD/pQ2=0.150 downstream D=3J6 inches, L/D=3.26.

L/D=7.15, SID/pQ =0.330

Figure 3. SWIRLING FLOW IN STRAIGHT TUBES

RESULTS

Flow patterns at low velocities were readily made visible with smoke. With

the inlet vanes in the radial position no rotation was imparted to the fluid and

streamlines in the test section were essentially straight and parrallel to the

tube centerline. With the vanes inclined slightly from the radial position

(discharge held constant) streamlines in the test Section became steady spirals.

That condition is shown in Figure 3a. Further closure of the vanes eventually

produced vortex breakdown. Figure 3b shows the stagnation point occurring near

the right quarter point of the tube with a helical vortex occurring downstream

from the stagnation point. Still further closure of the vanes moved the stagnation

point to the upstream limit of the tube. Figure 3c shows the helical vortex

filling the tube. A comparison of this helical vortex pattern.with those observed

below a turbine runner [2,8] establishes the similarity.

Although flow patterns could be observed only at la•+ velocities (below 5 feet

per second) unsteady pressures could be measured only at higher velocities. To

insure that similar flow patterns occurred at these higher velocities, a hot-

wire anemometer was used to measure air velocities near the tube wall and at the

tube centerline. These measurements showed that surging began at the same gate

setting (same QD/pQ2) regardless of discharge.

In the experiments pressure amplitudes and frequencies occurring after surg-

0 ing commenced were measured near the open end of the straight tubes, upstream

from the elbow of the draft tube, and near the entrance of the straight cone. The

onset of surging (vortex breakdown) was correlated with the value of QD/pQ2. It

was also found to be a function of L/D and shape. For the elbow draft-tube and

the straight cone the critical value of RD/pQ2 was 0.4. Above this value surging

occurred.

The dimensionless frequency and pressure parameters of Equations (1) and (2),

calculated from the experimental measurements, are shown in Figures (4) and (5).

These parameters were found to be independent of viscous effects for Reynolds

numbers greater than 1 x 105 and the results for smaller Reynolds numbers are not

shown here.

In order to obtain reproducible results, it was necessary to measure the

root-mean-square values of the pressure fluctuations and it is these values which

were used in the preparation of Figure 4. Straight tubes are seen to have

pressure characteristics which are strongly influenced by relative length. The

pressure characteristics of the elbow draft-tube and straight cone are striking

since the pressure parameters exhibit a maximum value as nD/pQ2 is made larger.

Frequencies of the unsteady pressure were quite regular and, thus, relatively

easy to measure. The regularity indicates that the helical vortex precesses about

the tube centerline at a reasonably regular rate. Figure (5) shows that the

divergent tubes significantly reduce the frequency of surging. However, the bend

in the draft tube has an insignificant effect upon frequency.

6 g 1

g~—

+ + +

2.0 Symbols Defined ++ + ;,1x

in Figure 5 - tCylindersl +4- x

+ x

+ °°° x Cone + .6p D4

o -1.29[I:1.108(P 2-1.41)] t x PQ2

1.0 . o

Ap D4 x °

• x • x x x

x

Q2 P x '• x

''-' XxElbow Draft Tube xA 4

xxxx P0=1.111:1.563 42 C

;;7 xx

0 0 1.0 12 D 2.0 3.0

PQ2 Fig. 4-PRESSURE PARAMETERS FOR SURGING

x x +

2.0 x +

x+ + I x + -

X + j

f D3 x +

x ~

Q ++

o° 1 °°

x °°O

1.0

•po as

D L/ D .521 ft. (15.9 cm) 4.68 Elbow Draft Tube

ebb ° .503ft.(15.3cm) 4.84Truncafed Cone 4-.511 ft (15.6 cm) 3.26 Circular Cylinder x .511 ft, (15.6cm) 1.63 Circular Cylinder

0 All Tubes Have Sharp edged Entrcnce5

0 1.0 a D 2.0 3.0 i

Fig. 5- FREQUENCY PARAMETERS FOR SURGING

7 E 1

ANALYSIS OF DRAFT-TUBE SURGING IN A TURBINE

• Occurrence and severity of draft-tube surging in a given hydraulic turbine

and associated draft tube can be predicted using the experimental results of this

study. To do this it is necessary to be able to compute the parameter PD/pQ2 of

the flow as it leaves the turbine runner and enters the draft tube.

Analysis of Turbine

Horsepower P imparted to the turbine runner by water flowing through it is

given by the classic expression

P rr -n z)15 (5) 60 In '

where n is the rotational speed of the turbine in revolutions per minute, and

Q2) is the rate of change in angular momentum occurring in the flow as it

passes through the runner. Subscripts 1 and 2 refer to the entrance and exit

sides of the runner respectively. Multiplying both sides of Equation (5) by

550 D/npQ2 and using Equation (4) yields

f12 D DRsina _550 P„ D ( 6 ) — P92 BN5 2V2-9,' P DZ

where ~, Pll, Qll, and D2 are respectively the specific speed, power, discharge

and runner diameter and are defined in Figure 6 and Q2D/pQ2 is the momentum para-

meter associated with the flow leaving the turbine runner and entering the draft

tube. The first term on the right of Equation (6) is the momentum parameter

associated with the flow leaving the wicket gates and entering the turbine and

can be evaluated if the wicket-gate geometry is known. The second term on the

right of Equation (6) can be evaluated if the performance characteristics and

9s geometry of the turbine are known..

Specific Application

Equation (6) was used to analyze the hydraulic turbine at Fontenelle Dam

[9]. The efficiency hill for the turbine, as determined from model tests, is

shown in Figure 6. Any point on this efficiency hill yields a particular value

Of Q2D/pQ2 and, thus, areas of potential surging--where E12D/pQ2 exceeds 0.4--can

be determined. Figure 7 shows the regions in which surging can be expected and

also shows a line representing operating conditions for which flow leaving the

turbine and entering the draft tube has zero swirl. To the left of this line flow

in the draft tube swirls opposite to the turbine rotation while to the right

swirl is with the runner. The point of maximum efficiency falls on the line of

zero swirl for this unit although this is not apparently true of all units.

Figure (4) predicts that for the elbow draft tube a maximum pressure ampli-

tude occurs at Q2D/pQ2 = 1.30. The line on which surging would produce this

maximum pressure amplitude is also shown on Figure 7. A parabolic curve was fit-

ted to the pressure data for the elbow draft tube. This parabolic expression

(shown in Figure 4)was used in conjunction with Equatim(6)tocalculate relativevalues

8 $ 1

O D2

i

090

80 17= 0/6Efficie cy 76

0 /

50 a 30 2 10 Runaway

~0 Speed P

P11=D2 HBO: e

N S = ~g ¢ P 2 =63 0 ~— n

0 1.0 7rD2 n 2.0

¢ 601. 2gH FIGURE 6 EFFICIENCY HILL FOR FONTENELLE TURBINE

2 .0

'17 900

F /

~c

c •may ~r • y i

o I.0 Zero Swirl—, g~

_ - Runaway v / Speed

\Maximum Surge Amplitude

01 0 1.0

De n 2.0

¢ 60'V29

FIGURE 7 PREDICTED SURGING FOR FONTENELLE TURBINE

9 $

(AP/pgH where H is net head on the unit) of pressure amplitudes for the Fontenelle

unit. The results of this computation are shown on Figure 8 along with relative

power swings actually measured at the plant. Excellent agreement is shown for

the wicket gate opening at which maximum surging occurred. Numerical agreement

of the % power swing and % pressure fluctuation was not expected because the

dynamics of the mechanical and electrical system are necessarily involved in

determining the power swing arising as a result of the pressure surging which is

the driving force. The lack of agreement occurring at each side of Figure 8 may

also be due to the use of Equation (4). Analysis of other units indicated that

this expression may not give an entirely accurate estimate of the momentum para-

meter for all gate openings usually because the exact geometry of the wicket gate

assembly is not accurately known.

CONCLUSIONS

A particular hydraulic turbine can be analyzed for possible surging within

the desired range of operation by the method presented herein. Dimensionless

frequencies and root-mean-square amplitudes of unsteady pressures measured herein

are directly convertible to prototype conditions by similitude considerations.

However, they can be expected to predict prototype conditions only for the "hard-

,r core" vortex condition. For low-tailwater conditions, for which the vortex core

becomes unwatered, a two-phase flow occurs and pressure surges are usually some-

what milder.

ACKNOWLEDGEMENTS

Mr. U. J. Palde of the Hydraulics Branch, U.S. Bureau of Reclamation, took

much of the data and carefully refined the experimental methods and equipment

used.

PPPrPrNrrcz

1.) Rheingans, W.J., "Power Swings in Hydroelectric Power Plants," Transactions,

American Society of Mechanical Engineers, Vol. 62, 1940.

2.) Hosoi, Y., "Experimental Investigations of Pressure Surge in Draft Tubes of

Francis Water Turbines," Hitachi Review, Volume 14, Number 12, 1965.

3.) Harvey, J.K., "Some Observation of the Breakdown Phenomenon," Journal of

Fluid Mechanics, Vol. 14, 1962.

4.) Chanaud, R.C., "Observations of Oscillatory Motion in Certain Swirling Flows,'

Journal of Fluid Mechanics, Vol. 21, 1965.

5.) Benjamin, T.B., "Theory of the Vortex Breakdown Phenomenon," Journal of

Fluid Mechanics, Vol. 14, 1962.

6.) Squire, H.B., "Analysis of the Vortex Breakdown Phenomenon, Part I," Aero

Department, Imperial College, Report Number 102, 1960.

10 B I

Fontenelle

relative

)wn for

ireement

the

!d in

which is

!re 8 may

ed that

um para-

cket gate

within

iless

M herein

Lions.

ie "hard-

:ex core

y some-

, took

ment

Rated Output=11.9 Mega-watts ~r~Predicted % Pressure Fluctuation

02.0 4 Net Head= 100 Feet

z

z ,Measured % Power ._0 1.5 3 Swing-

Peak to Peak

o + \ +

\

ti 1.0 ° 2 i

o S \

0.5 I / \

H o /

4 0 0 +

0 20 40 60

% Wicket Gate Opening

FIGURE 6 PREDICTED AND MEASURED SURGING EFFECTS

actions,

:bes of

I of

ig Flows,'

of

Aero

Contribution by 1. Raabe on Paper E1

Since the publication of Meldau:"Drallstrdmung im Drehhohlraum" in 1935

we know that steady potential flow in a straight tube with an axial

component and a circulation as Dr Falvey and Prof. Cassidy describe; is

usually connected with a dead water core.The ratio of core diameter

to internal tube diameter is controlled by the law of minimum of

kinetic flow energy content in the tube. This law is a special case

of the law of minimum resistance. Bamme-A and Kl&L&eY)s have enriched

1950 our knowledge of straight tubular potential flow with circulation

in so far as they stated and observed a back flow in the core for

those cases in which the pressure on the external boundary of the core

drops below the back pressure. In a longer tube with pressure losses

in axial direction this return of the flow in the core may happen at

variable stations on the axis.The position of this depends on circu-

lation and thrnughfloW.

to reality the dead water core is also set in~ otation by boundary

friction.Therefore it, can be taken as a vortex.Slight irregularities

in the axial flow with enlarged discharge displace the vortex center

from the axis. These irregularities belong strongly to the inlet

conditions in the tube.

Hereby the displaced vortex core element induces at other vortex core

elements a radial displacement. The displaced element does the same

with a following element, by this forming a helical vortex. This vohtex

rotates in circumferential direction in the sense of circulation of

the surrounding flow, also due to induced velocity. The tangential

induced velocity at any core element and its approximation to the wall

due to suction effect of surrounding flow enlarges the radial deviation

of the vortex core so that it touches the tube wall at last.This is

seen clearly by the 'experimehts of Dr Falvey and Prof. Cassidy.

They stated that viscosity the observed Reynolds number-off 105

is negligible. Therefore-rotational speed of thie--vortex and tie pressure

pulsations in connection herewith can only be controlled_by inertia—___.__

r

forces of rotating and axial-flow masses. Dimensionless pressure

amplitude and its frequency is therefore a function of dimensionless

ratio of kinetic energy of rotational and axial flow as formulae 1

and 2 show.

The dependence of the ratio Z/D and Reynolds number describes the

dependence of the flow returning point in the axis as function of

pressure drop as mentioned above.

The curiousity not known in real turbines seems to be that the f ormatic

of the helicoidal whirl begins at large distances from the inlet of

the tube. It is in contrast to the swirl of a turbine, beginning mostly

behind the runner, at the hub or in the runner itself.

The use of the model formula in the shell diagramm of a turbine

therefore rises some doubts:

1/ Flow in a turbine runner, especially a Francis runner of high

specific speed, can only be described by one circulation before and

behind the runner after thoroughful measurements of flow velocity at

these stations.

2/ Due to fig 4 pressure pulsation will be higher on a cylinder. This

in contrast to the experience that an internal coaxial cylindrical

tube in the draft tube quietens the pressure pulsations remarkably.

3/ Fig 7 shows surging regions but not the magnitude of pressure

pulsation. The limits of these regions are gained by equations 6

which uses the shell diagramm fig 6. This diagramm doesn't distinguish

a helical whirl region and a pulsating straight whirl region.

Especially the pulsations of a central whirl at higher discharges

with circulation against the speed causes the stronger shocks.

4/ From fig 5 follows for a runner with given D,N,B that

- - - -- — w-here W,,* gu e opening angle. is t e

For Francis turbines one can estimate

cos p(o — constant

By this

f H Observing

fn u

we have

f/n - constant

Concluding I can state that the air tests of the authors have a

preliminary value in predicting qualitatively the ep-region but not the exact strength of Qp. On behalf of a constant frequency/

speed ratio the paper may give some approximation to the prototype.

The resting guide apparatus with its wicket gates and its sharp

inlet edges in the tube doesn't coincide with the runner as the

real boundary condition.

SYMrU51UM 1970, STOCKHOLM

H. T. Falvey, J. J. Cassidy, "Frequency and Amplitude of Pressure Surges Generated by Swirling Flow"

t

DISCUSSION

by Rex A. Elder, Director,.TVA Engineering Laboratory, USA and Svein Vigander, Research Engineer, TVA Engineering Laboratory, USA

.The authors have presented model data in dimensionless form

from which the frequency and amplitude of pressure pulsations in

draft tubes of hydraulic turbines can be predicted. This type of

information is needed both to better understand the generation of pe-

riodicity in the swirling flow and to enable prediction of the fre-

quency and severity of disturbances to be expected in new turbine designs.

We would like to add a few comments based on the studies

made by TVA's Engineering Laboratory on the vibrations of a 36-MW

fixed-bladed turbine unit. Mention of these vibration studies were

made earlier, at the 1968 Lausanne Symposium and at the 13th Congress

in Kyoto.

On the enclosed Figure 1, we show the results of measure-

ments of pressure pulsations made at the draft tube man door below

the turbine runner. The pressure pulsations were measured with a

flush-mounted, diaphragm-type, electronic pressure transducer. The

data has been reduced to the dimensionless coordinates shown on the

author's Figure 4 and Figure 5. The applicable parts of these fig-

ures are also shown on the enclosed Figure 1. The prototype data

scatter right around the curves drawn through the model results for

both frequency and amplitude of pulsations. This agreement, we feel,

is quite remarkable, particularily in view of the fact that geometric

similarity between the model and the prototype in this case was lim-

ited to whatever is implied in the general phrase "Elbow Draft Tube".

In light of these results, it would be interesting to see data from

Fontenelle Dam and other dams plotted in a similar manner. We hope

that the addition of this information may make engineers even more

confident in the use of the author's results.

LL; 2.0 Lv , O U Q SNL

LLJ CURVE THROUGH 1.5 FALVEY AND CASSIDY'S

1— MODEL DATA s WHEELER UNIT 11

p GAGE P4 ON DRAFT

Q I.0 TUBE MANDOOR D

N p I SYMBOL TEST DATE O pp O ID p I O E2 9/67

N_ 0'S _

0 0 O E 8/67

C 1 8/67

0 0 0 0.5 1.0 1.5 2.5 2.5

I 100 70 50 40 30 25

PERCENT GATE OPENING

Mr. S. GASAuc;i

Doctor of Math Sciences Technical Director Energy Division

ALSTHOM - NEYRPIC

Grenoble - France

Remarks on report E1 of Mr. H.T. FALVEY and J.I. CASSIDY "Frequency and amplitude of pressure surges generated by

swirling flow"

The paper of Mr. Falvey and Mr. Cassidy comprises an interest-ing attempt to explain pressure surge phenomena which are pro-duced in the draft tubes of hydraulic turbines ; this explana-tion gives an account of the general aspect of their experimen-tal results.

On the characteristic hill curve of a Francis turbine, can indeed be seen a surge-free zone corresponding to slight swirling flow at the runner outlet. Outside this zone, swirl-ing flow appears rotating in the same direction as the runner or in the opposite direction,depending on whether the operatin,_ point happens to be above or below the surge-free zone.

Starting from the hill curve and knowing 521, it would be pos-sible to calculates 2, but it.is in fact very difficult to calculatenj from the geometry of the distributor. Moreover, Ao defined from the output corresponds to an overall value. There exist operating points where the water, leaving the run-ner, turns in one direction for one operating zone and in the other for another. When swirling flow appears at the runner outlet, what value must be chosen for n2 to define S22 D/pQ2:

On either side of the "calm" area, having an absolute compara-ble value n2 D/pQ2, the contoursof the axial velocities differ widely ; the stability conditions should not therefore be the same ; furthermore the distribution of the axial velocities in the model without a runner used by the authors is very diffe-rent from those of a model with a runner. It is worth pointing out that the vortices do not take the same form on each side of the swirl free zone : they are roughly axial for the large Q11 and helical for the small Q11. It seems therefore difficult to characterise the instability of a flow so complex by a sin-gle parameter SZD/pQ2.

The attached figure shows the distribution of axial velocities; at the draft tube inlet for various operating conditions. For points above and below the "calm" zone, the maximum axial velocities for this machine occur at the centre and near the draft tube wall respectively. For a givenSftD/pq2, the stabili-ty conditions for these two types of flow should be different.

It therefore seems that tests on _a model equipped with a run-ner are necessary to define the pressure surges and their transposition onto the prototype machine. The frequency of these pressure surges is of as much if not more interest than their amplitude. In fact, the problematical pressure fluctua-tions do not always have well defined frequencies. For partial loads, more or less periodic fluctuations can be noted ; the frequencies of the maximum amplitudes depend on the machine's speed of rotation and are little influenced by cavitation. For high loads, the frequencies, less well defined, are a functior of T. Their problematical character would require the use of the energy spectral densities and root mean square values. On this subject, the authors compare the peak-to-peak amplitude variations of the power fluctuations to the root mean square values calculated from the pressure surges. In fact, the root mean square values should be compared, allowing for the trans-fer function linking the variations in output to the variatiot in pressure in the draft tube, considered as the only importai disturbances. Readings taken on industrial machines do seem tc indicate that the spectral densities relating to shaft torque variations are difficult to link to those concerning draft tui pressure fluctuations.

Finally, it must be stressed that it is the whole range of frequencies of several tens of Hertz and under which is of practical interest and not the lowest frequencies of about 1 Hertz. Knowledge of this frequency range also requires test! on a complete turbine model.

r

a,) ofri

- - - ~• ~ X ~~Ilaljirilgr

~i.,~l 1 ~Nlti

- ~% i`-

~ 13

66*76

84.

i I 4 r

• j j i ~ O 11 t

r — Sens rc

DISCHARGE DISTRIBOTIC

,AND FLOW ROTAT ION BE LOW THE RUNNER

r

DISCUSSION TO PAPER El BY CASSIDY AND FALVEY:

Authors' Reply by John J. Cassidy and Henry T. Falvey

It is both frustrating and rewarding to receive a wealth of

discussion to one's paper. We have demonstrated a basic approach

to the analysis of an old problem. Because the problem is indeed

complex and has received attention from many investigators over

at least four decades, it was natural that both favorable and un-

favorable comments should arise. The authors' contention is simply

that draft-tube surging is a fluid-flow phenomenon and as such must

by analyzed in terms of fluid-flow parameters. The hvdraulic tur-

bine, as a machine, changes not only the energy content of the water

as it passes through the runner but the momentum content and dis-'

tribution as well. We will attempt to answer each discusser's com-

ments in the light of our contention.

The prototype measurements plotted in accordance with our pa-

rameters and presented by Elder and Vigander were quite encouraging.

However, in their Fig. 1 (Draft-tube pressure pulsations) the curve

denoted as "curve through Falvey and Cassidy's model data" should

not pass through the origin of the plot of f Dyp versus rL D/I.Q? The critical value of .C1D1 QZ as measured by the authors was 0.4

below which surging did not occur. A drawing showing the geometry

of the Fontennelle draft is included in this reply. Unquestionably

the shape of the draft tube has an effect upon both the occurrence

and the magnitude of pressure surges. This effect of shape is one

which should receive considerably more attention,

NOHABfs measurements as presented by Mr. Holmen provide an ex-

tremely gratifying support and simultaneously illustrate the impor-

tance of the plant 6 or cavitation coefficient. The effect of 6

was alluded to in t^e author's paper but could not be supported with

data. Mr. HoL„en's results show that as 6 decreases the amplitude

of the pressure surge decreases. It is the author's contention

that as 6 is reduced the flow becomes two-phase to an increasing

degree. Because of the rotation in the draft all air and vapor mi-

grate to the tube- center: . Appa-ren-tly this -e-f~-ect stabilizes the vortex. This 6 effect is in keeping with the field observation that

A, ,

rging is alleviated when tail-water elevation is decreased or when

L, is injected into the draft tube. The authors deliberately chose

r as the medium for our study in order to eliminate C as one of

a important parameters. However, detailed study of the effect of

6 is certainly desirable and is a logical second step in the inves-

tigation of draft-tube surging.

Dr. Casacci makes several interesting points. In a given hydro-

electric plant it is possible for resonance to occur in the penstock,

the electrical network, the governor system, or in a combination of

all. However, the draft-tube surge frequency is the driving fre-

quency and its use is mandatory in a study of possible resonance

conditions. For the Fontenelle-dam surge tanks prevented penstock

resonance and the plant output of approximately 10 megawatts is

negligible as compared to the connecting system. Resonance was not

expected and, thus, it is not surprising that- the maximum power

swing coincided with the gate opening producing the maximum ampli-

tude of pressure surge.

The calculation of SLZD0 QZ seems to raise difficulty but not in the way Dr. Casacci questions. Equation (6) is a momentum equation

and is, thus, affected only by forces which produce a torque. Re-

gardless of what the velocity distribution is at the draft-tube en-

trance ilzQ~po" will be correct if S11 D~PQ'' and turbine characteristics are correct. Equation (4) gives a reasonable value for 111 D/14L in all cases we have studied.

The effect of velocity distribution on the critical value of

tLZp,P is certainly a valid question. It was also of considerable

concern in our study. In our complete study (Journal of Fluid

Mechanics (1970), vol. 41, part 4, pp. 727-730) we deliberately

varied-the inlet geometry so as to vary the inlet-velocity distri-

bution. No apparent effect on the critical value of R,D~PQZ was

noted. We conclude, therefore, that there is a unique flow pattern

for a given value of n2D/PQZ even though the development of the flow pattern may differ. - " -

Dr. Casacci's statement that dynamic characteristics of shaft

torque characteristics care. difficult to link to the frequencies of

the draft-tube surges is in contradiction to other studies. One

thing we have often noted is that pressure taps in prototype draft

tubes frequently are located where eddies shed from upstream geometry

are measured rather than the pressure surge of interest. Also, the

dynamic effect of the connecting electrical system frequently plays

an important part in determining the generator motion and hence the

shaft torque.

Professor Raabe questions essentially the validity of our con-

tention that "vortex breakdowns' and draft-tube surging are one and

the same. Our observations as seen in Fig. 3 show the flow pattern

in each to be the same. Simultaneous measurements of pressure and

velocity show that the unsteady pressure is due to an unsteady

velocity. Observations of flow patterns at low velocities and pres-

sures at high velocities show that surging occurs at the same value

of-Q2. 0/10 regardless of the magnitude of Q (with some allowances

for Reynolds number effect). Prototype measurements and independent

measurements in other laboratories support our contention. Therefore,

we rest our case.

Placing a coaxial cylinder in a draft tube alleviates surging

because it effectively decreases -UD11oQz since the effective diameter

D is decreased.

Finally, some observations should be made relative to further

study of draft-tube surging. Fixed-blade turbines will always impart

angular momentum to the flow entering the draft tube at some settings.

It is logical that some changes in runners can be made to improve on

surging characteristics. This, however, will probably reach the

point of diminishing returns quite rapidly. It would appear that

changes in draft-tube design offer the greatest possibility for

improvement. In this light, the effect of divergence of the draft

tube is currently under study. However, even more imaginative

studies should be pursued. Presently, draft-tube designs are satis-

factory only when the turbine is operating at maximum efficiency.

However, operation is most frequent at conditions other than maximum

' efficiency for which flow is frequently upstream in one half of the

draft tube. For high-head plants, surging might well be avoided

entirely if no-draft tube--were provided and efficiency would- be

changed very little percentage-wise. In short, it would seem that

less attention could be paid to the peak efficiency and more to

other operationai cnaracteristics.

D~ 10.0'

Aff

4 M

~ 3 Pier Gate

Ki Nose slot

2

A~ 3- / / Half Cone Angle =

L /D3

2 3 4 5

- -1.03 D3

D3~

Figure/ Fontene/% Draft Tube